Evidence of a decrease of khz quasi-periodic oscillation peak separation towards low frequencies in 4U (GX 354 0)

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1 Mon. Not. R. Astron. Soc. 345, (2003) Evidence of a decrease of khz quasi-periodic oscillation peak separation towards low frequencies in 4U (GX 354 0) S. Migliari, M. van der Klis and R. P. Fender Astronomical Institute Anton Pannekoek, Universityof Amsterdam, and Center for High Energy Astrophysics, Kruislaan 403, 1098 SJ, Amsterdam, the Netherlands Accepted 2003 September 8. Received 2003 September 8; in original form 2003 July 24 1 INTRODUCTION ow-mass X-ray binary (MXB) low-magnetic field neutron stars (NSs) often show pairs of khz quasi-periodic oscillations (QPOs) in their power spectra. The frequency separation ν between these twin peaks is sometimes observed to be close to the burst oscillation frequency ν burst, interpreted as the spin frequency of the NS (Strohmayer et al. (1996); see Chakrabarty et al. (2003)), while sometimes it is close to half of it. Recent work on the millisecond pulsar SAX J (where the spin frequency is measured more straightforwardly, at 401 Hz; Wijnands et al. 2003) indicates that in those latter cases, ν is half the spin frequency. In some perhaps all sources, ν decreases significantly with increasing quasi-periodic oscillation (QPO) frequency. GX 17+2 shows a hint of a decrease at lower frequencies (Homan et al. 2002), but is consistent with being constant. In some sources for example, 4U (Méndez & van der Klis 1999) the peak separation is always significantly lower than the burst oscillation ν burst, whereas in 4U (Jonker, Méndez & van der Klis 2002), ν varies between lower and higher than ν burst /2. Two competing interpretations exist for these high frequency timing features (for a review, see van der Klis 2000, and references therein), which make definite predictions for ν. The relativistic precession model (RPM: Stella & Vietri 1998, 1999) is based on migliari@science.uva.nl ABSTRACT We have produced the colour colour diagram of all the observations of 4U available in the Rossi X-ray Timing Explorer public archive (from 1996 to 2002) and found observations filling in a previously reported gap between the island and the banana X-ray states. We have made timing analysis of these gap observations and found, in one observation, two simultaneous khz quasi-periodic oscillations (QPOs). The timing parameters of these khz QPOs fit in the overall trend of the source. The lower khz QPO has a centroid frequency of 308 Hz. This is the lowest lower khz QPO frequency ever observed in 4U The peak frequency separation between the upper and the lower khz QPO is ν = 274 ± 11 Hz, significantly smaller than the constant value of ν 350 Hz found when the lower khz QPO frequency is between 500 and 800 Hz. This is the first indication in this source for a significant decrease of khz QPO peak separation towards low frequencies. We compare the result briefly to theoretical models for khz QPO production. Key words: accretion, accretion discs binaries: close stars: individual: 4U stars: neutron. free test particle orbits around a compact object. This model identifies the upper khz QPO as the frequency of an orbit in the disc and the lower khz QPO with the periastron precession of this orbit. The RPM model predicts that the frequency separation ν decreases both when the khz QPO frequencies increase (as observed), but also when they decrease to sufficiently low frequencies. In the sonic-point beat-frequency model (SPBFM: Miller, amb & Psaltis 1998), an orbiting clump at the sonic radius is related to the production of the upper khz QPO and the beat between this clump and the NS spin frequency produces the lower khz QPO. In this model, ν should be equal to the spin frequency in principle, but can decrease when the upper khz QPO increases as a result of the spiral-in of the clump. So, both theoretical models (RPM and SPBMF) can explain the observed decrease of ν with increasing QPO frequency. What evidence can constrain or test the validity of the models? The two models predict different behaviours of ν as the khz QPO frequencies decrease: the RPM predicts a decrease of ν, whereas the beat-frequency model predicts a steady or increasing (see, for example, the discussion in Jonker et al. 2002) peak separation. In addition, Osherovich & Titarchuk (1999) developed the two-oscillator model, which explained the khz QPOs as arising from oscillations of hot blobs thrown into the magnetosphere of the NS. They identify the lower khz QPO frequency as the Keplerian frequency of the blob and the upper khz QPO frequency as the radial oscillator mode frequency, a non-linear function of the Keplerian frequency. This model also gives a relation between the lower and the upper khz QPOs (dependent on the source; see, for C 2003 RAS

2 36 S. Migliari, M. van der Klis and R. P. Fender example, Titarchuk, Osherovich & Kuznetsov 1999) which can be tested by observations. In this etter, we present the timing analysis of recent observations of the MXB 4U We find twin peaks with lower khz QPO frequency as low as 308 Hz, and the first indication for a significant decrease of the khz QPO peak separation as the khz QPO frequencies decrease. If confirmed, this evidence will constrain theoretical models strongly and, in particular, rule out the SPBFM in its current formulation U U (GX 354 0; Forman, Tananbaum & Jones 1976) is a low-mass X-ray binary and type I X-ray burster (ewin, Clark & Doty; Hoffman et al. 1976), identifying the accreting compact object as a neutron star. Hasinger & van der Klis (1989) classified 4U as an atoll-type X-ray binary. Strohmayer et al. (1996) found slightly drifting oscillations at 363 Hz during X-ray bursts, interpreted as the spin frequency of the NS. At high frequencies, the source shows khz QPOs up to 1200 Hz (Strohmayer, Zhang & Swank 1997), often in pairs (lower and upper khz QPOs). These pairs have a frequency separation ν almost constant at 350 Hz (i.e. significantly lower than the spin frequency) for lower khz QPOs between 500 and 800 Hz, decreasing significantly to ν 280 Hz above 800 Hz (Méndez & van der Klis 1999). No twin peaks with a lower khz QPO frequency lower than 500 Hz have been found in 4U until now. 2 OBSERVATIONS AND DATA ANAYSIS We have made timing analysis of 4U data from 1999 to 2002 performed using the Proportional Counter Array (PCA) instrument on the Rossi X-ray Timing Explorer (RXTE) satellite. 2.1 Colour colour diagram We have used Standard2 data of the Proportional Counter Unit 2 (PCU2, always on in all epochs) to produce the colour colour diagram (CD) of all the observations available in the RXTE public archive (from 1996 to 2002). The soft colour and the hard colour are defined as the count rate ratio (3.5 6) kev/(2 3.5) kev and (9.7 16) kev/(6 9.7) kev, respectively. We have normalized the colours of 4U to the colours of the Crab calculated with the closest observation available to each 4U observation. In Fig. 1, we show the mean colours of all the observations of 4U as dots; squares are the observations ( ) previously analysed by Di Salvo et al. (2001) and van Straaten et al. (2002); and the circle marks the observation where we find significant khz twin peaks (see below). Di Salvo et al. (2000) found a gap in the CD between the island state and the banana state. This gap was only due to lack of observations. We concentrate on the observations filling in this gap in between island and banana, namely in the range of the hard colour. 2.2 Timing analysis For the production of the power spectra we have used event data with a time resolution of 125 µs. We rebinned the data in time to obtain a Nyquist frequency of 4096 Hz. For each observation, we created eahy et al. (1983) normalized power spectra from segments of 16-s length. We removed dropouts and X-ray bursts from the data, but no background and deadtime corrections were performed. We Figure 1. X-ray colour colour diagram (CD) of all the RXTE/PCA (PCU2 only) observations of 4U available in the public archive: soft colour = 3.5 6) kev/(2 3.5) kev, hard colour = ) kev/(6 9.7) kev. Plotted are the mean colours of each observation. The squares mark the observation until 1997 analysed by Di Salvo et al. (2000) and van Straaten et al. (2001); the circle marks the gap observation which shows khz twin peaks (with typical 90 per cent error bars indicated) averaged the power spectra and subtracted Poisson noise spectrum according to Zhang et al. (1995), shifted in power to match the spectrum between 3000 and 4000 Hz, where there should be no timing features. Then we converted the power spectra to squared fractional rms. We have fitted the power spectra with a multi-orentzian model (for details, see Belloni, Psaltis & van der Klis 2002 and references therein). The power spectra of the gap observations are fitted using one broad orentzian ( b or b2 ) to represent the low-frequency noise and the break frequency; one ( h )ortwo( b and h ) narrower orentzians between Hz; a broad orentzian around 100 Hz ( hhz ); and one (except two observations in which two are needed, i.e. with a single-trial significance >3σ ; see Section 3) narrow orentzian to fit the upper khz QPO u in the range Hz (see van Straaten, van der Klis & Méndez 2003 for details on terminology). 3 RESUTS Fig. 2 shows a typical power spectrum of the observations analysed, with the best-fitting model. The upper khz QPO is present in 46 out of 48 observations. The power spectra are consistent with those found around this position in the CD by Di Salvo et al. (2000) and van Straaten et al. (2001; see their fig. 1, panel 7). In two observations, namely and , we observe both the lower ( l ) and the upper khz QPO. In , l and u are single-trial significant (see Section 3.1) at a 4.4σ and 7.9σ level, respectively. In , the significance is 4.5σ for the lower khz QPO and 3.4σ for the upper khz QPO. Another observation ( ) shows a less significant (2.3σ ) lower khz QPO (the upper khz QPO is significant at 10σ ). In the observation (see Fig. 3), the centroid frequencies of the lower and the upper khz QPOs are ν l = 308±5Hzandν u = 582±10 Hz, respectively. The peak separation is ν = 274 ± 11. In the observation , the centroid frequencies of the lower and the upper khz QPOs are ν l = 385 ± 9Hzandν u = 616 ± 19 Hz, respectively. The peak separation is ν = 231 ± 21. To check for frequency variations in the khz peaks, we divided observation

3 khz QPOs peak separation in 4U b2 b h hhz u b h hhz l u Figure 2. Typical power spectrum of a gap observation (i.e. observation ) with the best-fit multi-orentzian model into four time segments and observation into two segments, and analysed the power spectra of these segments. We note that is naturally divided in two by an X-ray burst; hence, in this case, we have analysed the pre-burst and post-burst power spectra. No significant frequency variations are present in either observation. 3.1 Trials and significance of the khz QPOs The number of gap observations analysed (observations with the hard colour in the range and with event data with a time resolution of 125 µs) is 48. When we look for a timing feature, the probability of a statistical fluctuation in the power spectrum at a certain frequency increases with the number of trials, i.e. with the number of power spectra searched, and with the range of frequencies ν range in which we expect the QPO. We estimate the total number of trials as number of power spectra ν range /FWHM. As reported in Fig. 3, in observation , we have a very significant upper khz QPO at 582 Hz. We expect the lower khz QPO (which has a FWHM 45 Hz) in an interval of frequencies of about 200 Hz. This leads to ν range /FWHM σ single-trial significance means a chance probability of , which, multiplied by 48 trials and by 4.4, gives : the QPO is still significant at a 3σ level. The khz QPOs at 385 and 615 Hz of the observation turn out to be only marginally significant below 3σ. Therefore, only one gap observation can be reported to show evidence of twin peaks in the power spectrum. 4 DISCUSSION We have analysed the observations of 4U , filling in the gap in the CD (found by Di Salvo et al. 2001) in between island and banana, namely in the range of the hard colour (see Fig. 1). In one of these observations, we find two significant khz QPOs with a lower khz QPO as low as 308 Hz (the lowest lower khz QPO l Figure 3. Top panel: the power spectrum, in the power multiplied by frequency representation, of the observation with the best-fit multi-orentzian model. Bottom panel: high-frequency range power spectrum of the same observation, showing the lower and upper khz QPOs. ever found in this source). The lower khz QPO has an amplitude of 5.9 ± 0.8 per cent (rms) and Q = ν 0 /FWHM = 6.9 ± 2.5; the upper khz QPO has 12.8 ± 0.8 per cent rms and Q = 2.9 ± 0.5. Do these features fit in the overall timing behaviour of the source? The amplitudes versus ν max of the khz QPOs of 4U are shown in fig. 1 of Méndez & van der Klis (2001). The lower and the upper khz QPOs form two distinct traces in the plot; we find that the upper khz QPO fits perfectly in the upper khz QPO trace. The lower khz QPO appears to be discrepant, but there are no other lower khz QPO measurements below 600 khz with which to compare. u

4 38 S. Migliari, M. van der Klis and R. P. Fender Figure 4. Characteristic frequencies (ν max ) of the orentzians used to fit the power spectra of 4U and the ν max of the upper khz QPO (ν u max ). The grey points are from van Straaten et al. (2002); the black points are from the observation The circles mark the b2, the triangles mark the b, the crosses mark the h, the squares mark the hhz and the diamonds mark the l. Comparison of the upper khz QPO frequency with the Q and amplitude of both the upper and lower khz QPOs (see fig. 4 in van Straaten et al. 2002) shows that all the parameters of these QPOs fit in the overall trend of the source. In Fig. 4, we show the characteristic frequency ν max (see Belloni et al 2001) of the upper khz QPOs (ν u max ) as a function of the ν max of all the other components used to fit the power spectra of 4U The grey points are from van Straaten et al. (2002) and the black points are from the observation The upper khz QPO frequency of the observation is consistent with the correlations found with all the other components and, in particular, extend the l u correlation (stars) to lower frequencies. The location of l at ν lmax = 308 ± 5Hz is too high for a hhz QPO, which, in any case, is detected separately (Fig. 3). Whether or not the gap in the l u correlation (diamonds in Fig. 4) between Hz is real must be investigated further. Clearly, bridging this gap would increase our confidence in the identification of the peak at 308 Hz. The peak separation of the khz QPOs we have found ( 275 Hz) is significantly lower than both the spin frequency as inferred by burst oscillations ( 363 Hz; Strohmayer et al. 1996) and the saturation value (at 349 Hz) found by Méndez & van der Klis (1999) in the range Hz. In Fig. 5, we show the peak frequency separation ν as a function of the lower khz QPO frequency. Filled circles are from Méndez & van der Klis (1999) and the empty circle is our observation. The solid line indicates the frequency of the burst oscillations at Hz (Strohmayer et al. 1996). This indicates a decrease of the peak frequency separation at low frequencies. This decrease is contrary to what is expected from the SPBFM, which predicts a steady or increasing peak frequency separation at low frequencies (see e.g. fig. 2 in amb & Miller 2001). A clear prediction of a decrease of ν is made by the RPM. However, it seems that the decrease at low frequencies we find is steeper than the one predicted by the RPM: see, for example, fig. 1 in Stella & Vietri (1999). We have also checked the relation between the upper and lower khz QPOs as predicted by the two-oscillator model. We have used the values of the constant parameters of equation (15) in Osherovich & Titarchuk (1999) as determined by Titarchuk et al. Figure 5. Frequency separation between the lower and the upper khz QPO as a function of the frequency of the lower khz QPO. The filled circles are from Méndez & van der Klis (1999), the empty circle marks the khz peaks we have found and the solid line indicates the frequency of the burst oscillations at Hz (Strohmayer et al. 1996). (1999) for 4U For a low-frequency QPO of 308 Hz the two-oscillator model predicts an upper khz QPO of 717 Hz, much higher than the one observed. ACKNOWEDGMENTS SM would like to thank Steve van Straaten, Tiziana Di Salvo and Mariano Méndez for very helpful discussions. We would like to thank the anonymous referee for her/his comments and suggestions. REFERENCES Belloni T., Psaltis D., van der Klis M., 2002, ApJ, 572, 392 Chakrabarty D., Morgan E. H., Muno M. P., Galloway D. K., Wijnands R. A. D., van der Klis M., Markwardt C. B., 2003, Nat, 424, 42 Di Salvo T., Méndez M., van der Klis M., Ford E., Robba N. R., 2001, ApJ, 546, 1107 Forman W., Tananbaum H., Jones C., 1976, ApJ, 206, 29 Hasinger G., van der Klis M., 1989, A&A, 225, 79 Hoffman J. A., ewin W. H. G., Doty J., Hearn D. R., Clark G. W., Jernigan G., i F. K., 1976, ApJ, 210, 13 Homan J., van der Klis M., Jonker P. G., Wijnands R., Kuulkers E., Méndez M., ewin W. H. G., 2002, ApJ, 568, 878 Jonker P. G., Méndez M., van der Klis M., 2002, MNRAS, 336, 1 amb F. K., Miller M. C., 2001, ApJ, 554, 1210 eahy D. A., Darbro W., Elsner R. F., Weisskopf M. C., Kahn S., Sutherland P. G., Grindlay J. E., 1983, ApJ, 266, 160 ewin W. H. G., Clark G. W., Doty J., 1974, IAU Circ., 2922 Méndez M., van der Klis M., 1999, ApJ, 517, 51 Méndez M., van der Klis M., Ford E. C., 2001, ApJ, 561, 1016 Miller M. C., amb F. K., Psaltis D., 1998, ApJ, 508, 791 Osherovich V., Titarchuk., 1999, ApJ, 522, 113 Stella., Vietri M., 1998, ApJ, 492, 59 Stella., Vietri M., 1999, Phys. Rev. ett., 82, 17 Strohmayer T. E., Zhang W., Swank J. H., Smale A., Titarchuk., Day C., ee U., 1996, ApJ, 469, 9 Strohmayer T. E., Zhang W., Swank J. H., 1997, ApJ, 487, 77 Titarchuk., Osherovich V., Kuznetsov S., 1999, ApJ, 525, 129

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